Deep neural networks trained with gradient descent exhibit varying rates of learning for different patterns. However, the complexity of fitting models to data makes direct elucidation of the dynamics of learned patterns challenging. To circumvent this, many works have opted to characterize phases of learning through summary statistics known as order parameters. In this work, we propose a unifying framework for constructing order parameters based on the Neural Tangent Kernel (NTK), in which the relationship with the data set is more transparent. In particular, we derive a local approximation of the NTK for a class of deep regression models (SIRENs) trained to reconstruct natural images. In so doing, we analytically connect three seemingly distinct phase transitions: the emergence of wave patterns in residuals (a novel observation), loss rate collapse, and NTK alignment. Our results provide a dynamical perspective on the observed biases of SIRENs, and deep image regression models more generally.

Moreo randominitializationH( 0)conv deterministic H asthewidthNeur ker ( , ) (Equation (2)) evaluatedH(t)= H forallt, then (3) becomes du(t) dt = H (u(t) y). Suppose (z)= max ( 0,z), 1/ = poly ( 1/ ,log (n / )) and d1 = d2 = = dL = m with m poly ( 1/ , L,1/ 0,n,log ( 1/ )).

The Neural Tangent Kernel (NTK) characterizes the behavior of infinitely-wide neural networks trained under least squares loss by gradient descent. Recent works also report that NTK regression can outperform finitely-wide neural networks trained on small-scale datasets. However, the computational complexity of kernel methods has limited its use in large-scale learning tasks. To accelerate learning with NTK, we design a near input-sparsity time approximation algorithm for NTK, by sketching the polynomial expansions of arc-cosine kernels: our sketch for the convolutional counterpart of NTK (CNTK) can transform any image using a linear runtime in the number of pixels. Furthermore, we prove a spectral approximation guarantee for the NTK matrix, by combining random features (based on leverage score sampling) of the arc-cosine kernels with a sketching algorithm. We benchmark our methods on various large-scale regression and classification tasks and show that a linear regressor trained on our CNTK features matches the accuracy of exact CNTK on CIFAR-10 dataset while achieving 150x speedup.

How well does a classic deep net architecture like AlexNet or VGG19 classify on a standard dataset such as CIFAR-10 when its "width"-- namely, number of channels

Understanding the spatial and temporal patterns of environmental exposure to radio-frequency electromagnetic fields (RF-EMF) is essential for conducting risk assessments. These assessments aim to explore potential connections between RF-EMF exposure and its effects on human health, as well as on wildlife and plant life. Existing research has used different machine learning tools for EMF exposure estimation; however, a comparative analysis of these techniques is required to better understand their performance for real-world datasets. In this work, we present both finite and infinite-width convolutional network-based methods to estimate and assess EMF exposure levels from 70 real-world sensors in Lille, France. A comparative analysis has been conducted to analyze the performance of the methods' execution time and estimation accuracy. To improve estimation accuracy for higher-resolution grids, we utilized a preconditioned gradient descent method for kernel estimation. Root Mean Square Error (RMSE) is used as the evaluation criterion for comparing the performance of these deep learning models.